Why is an object still moving even if force applied is equal to friction? Why is an object still moving even if force applied is equal to friction? If this force of friction is the same as the force applied, shouldn't the object be stationary instead? 
 A: It takes a net force to get a stationary object moving or to increase the velocity of an object already in motion (accelerate an object). It takes a net force to reduce the velocity of an object already in motion (decelerate an object) or to bring it to a stop. These observations are reflected by Newton’s laws of motion.
Therefore  an object at rest or already in uniform motion (zero or constant velocity and therefore zero acceleration) remains so unless acted on by a net external force. This is Newton’s first law and a consequence of $a=0$ in Newton’s second law $F_{net}=ma$
Applying these laws to your object, a net force (applied force greater than friction force) is required to accelerate the object and net force (applied force less than the friction force) is required to decelerate the object (slow it down), but a net force is not required to keep the object moving at constant velocity once it is in motion.
Hope this helps.
A: Assume an object is moving at $t=t_0$, at velocity $v_0$. Furthermore, the friction force $F_f$ is matched precisely by an externally applied force $F_e$ , so that $F_f=F_e$.
The net force acting on the object is thus:
$$F=F_f-F_e=0$$
According to N2L, then:
$$F=ma=0 \Rightarrow a=0$$
Without acceleration, the object will 'forever' maintain its initial velocity $v_0$, because $a=0$.
